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CorrelatedRandomVectorGenerator (Commons Math 3.2 API)
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org.apache.commons.math3.random</FONT>
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Class CorrelatedRandomVectorGenerator</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.random.CorrelatedRandomVectorGenerator</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math3.random">RandomVectorGenerator</A></DD>
</DL>
<HR>
<DL>
<DT><PRE>public class <B>CorrelatedRandomVectorGenerator</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A><DT>implements <A HREF="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math3.random">RandomVectorGenerator</A></DL>
</PRE>

<P>
A <A HREF="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math3.random"><CODE>RandomVectorGenerator</CODE></A> that generates vectors with with
 correlated components.
 <p>Random vectors with correlated components are built by combining
 the uncorrelated components of another random vector in such a way that
 the resulting correlations are the ones specified by a positive
 definite covariance matrix.</p>
 <p>The main use for correlated random vector generation is for Monte-Carlo
 simulation of physical problems with several variables, for example to
 generate error vectors to be added to a nominal vector. A particularly
 interesting case is when the generated vector should be drawn from a <a
 href="http://en.wikipedia.org/wiki/Multivariate_normal_distribution">
 Multivariate Normal Distribution</a>. The approach using a Cholesky
 decomposition is quite usual in this case. However, it can be extended
 to other cases as long as the underlying random generator provides
 <A HREF="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random"><CODE>normalized values</CODE></A> like <A HREF="../../../../../org/apache/commons/math3/random/GaussianRandomGenerator.html" title="class in org.apache.commons.math3.random"><CODE>GaussianRandomGenerator</CODE></A> or <A HREF="../../../../../org/apache/commons/math3/random/UniformRandomGenerator.html" title="class in org.apache.commons.math3.random"><CODE>UniformRandomGenerator</CODE></A>.</p>
 <p>Sometimes, the covariance matrix for a given simulation is not
 strictly positive definite. This means that the correlations are
 not all independent from each other. In this case, however, the non
 strictly positive elements found during the Cholesky decomposition
 of the covariance matrix should not be negative either, they
 should be null. Another non-conventional extension handling this case
 is used here. Rather than computing <code>C = U<sup>T</sup>.U</code>
 where <code>C</code> is the covariance matrix and <code>U</code>
 is an upper-triangular matrix, we compute <code>C = B.B<sup>T</sup></code>
 where <code>B</code> is a rectangular matrix having
 more rows than columns. The number of columns of <code>B</code> is
 the rank of the covariance matrix, and it is the dimension of the
 uncorrelated random vector that is needed to compute the component
 of the correlated vector. This class handles this situation
 automatically.</p>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>1.2</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: CorrelatedRandomVectorGenerator.java 1416643 2012-12-03 19:37:14Z tn $</DD>
</DL>
<HR>

<P>

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<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#CorrelatedRandomVectorGenerator(double[], org.apache.commons.math3.linear.RealMatrix, double, org.apache.commons.math3.random.NormalizedRandomGenerator)">CorrelatedRandomVectorGenerator</A></B>(double[]&nbsp;mean,
                                <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;covariance,
                                double&nbsp;small,
                                <A HREF="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</A>&nbsp;generator)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Builds a correlated random vector generator from its mean
 vector and covariance matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#CorrelatedRandomVectorGenerator(org.apache.commons.math3.linear.RealMatrix, double, org.apache.commons.math3.random.NormalizedRandomGenerator)">CorrelatedRandomVectorGenerator</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;covariance,
                                double&nbsp;small,
                                <A HREF="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</A>&nbsp;generator)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Builds a null mean random correlated vector generator from its
 covariance matrix.</TD>
</TR>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#getGenerator()">getGenerator</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the underlying normalized components generator.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#getRank()">getRank</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the rank of the covariance matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#getRootMatrix()">getRootMatrix</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the root of the covariance matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#nextVector()">nextVector</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Generate a correlated random vector.</TD>
</TR>
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<A NAME="CorrelatedRandomVectorGenerator(double[], org.apache.commons.math3.linear.RealMatrix, double, org.apache.commons.math3.random.NormalizedRandomGenerator)"><!-- --></A><H3>
CorrelatedRandomVectorGenerator</H3>
<PRE>
public <B>CorrelatedRandomVectorGenerator</B>(double[]&nbsp;mean,
                                       <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;covariance,
                                       double&nbsp;small,
                                       <A HREF="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</A>&nbsp;generator)</PRE>
<DL>
<DD>Builds a correlated random vector generator from its mean
 vector and covariance matrix.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>mean</CODE> - Expected mean values for all components.<DD><CODE>covariance</CODE> - Covariance matrix.<DD><CODE>small</CODE> - Diagonal elements threshold under which  column are
 considered to be dependent on previous ones and are discarded<DD><CODE>generator</CODE> - underlying generator for uncorrelated normalized
 components.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</A></CODE> - if the covariance matrix is not strictly positive definite.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the mean and covariance
 arrays dimensions do not match.</DL>
</DL>
<HR>

<A NAME="CorrelatedRandomVectorGenerator(org.apache.commons.math3.linear.RealMatrix, double, org.apache.commons.math3.random.NormalizedRandomGenerator)"><!-- --></A><H3>
CorrelatedRandomVectorGenerator</H3>
<PRE>
public <B>CorrelatedRandomVectorGenerator</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;covariance,
                                       double&nbsp;small,
                                       <A HREF="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</A>&nbsp;generator)</PRE>
<DL>
<DD>Builds a null mean random correlated vector generator from its
 covariance matrix.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>covariance</CODE> - Covariance matrix.<DD><CODE>small</CODE> - Diagonal elements threshold under which  column are
 considered to be dependent on previous ones and are discarded.<DD><CODE>generator</CODE> - Underlying generator for uncorrelated normalized
 components.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</A></CODE> - if the covariance matrix is not strictly positive definite.</DL>
</DL>

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<A NAME="getGenerator()"><!-- --></A><H3>
getGenerator</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math3.random">NormalizedRandomGenerator</A> <B>getGenerator</B>()</PRE>
<DL>
<DD>Get the underlying normalized components generator.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>underlying uncorrelated components generator</DL>
</DD>
</DL>
<HR>

<A NAME="getRank()"><!-- --></A><H3>
getRank</H3>
<PRE>
public int <B>getRank</B>()</PRE>
<DL>
<DD>Get the rank of the covariance matrix.
 The rank is the number of independent rows in the covariance
 matrix, it is also the number of columns of the root matrix.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>rank of the square matrix.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#getRootMatrix()"><CODE>getRootMatrix()</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="getRootMatrix()"><!-- --></A><H3>
getRootMatrix</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>getRootMatrix</B>()</PRE>
<DL>
<DD>Get the root of the covariance matrix.
 The root is the rectangular matrix <code>B</code> such that
 the covariance matrix is equal to <code>B.B<sup>T</sup></code>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>root of the square matrix<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html#getRank()"><CODE>getRank()</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="nextVector()"><!-- --></A><H3>
nextVector</H3>
<PRE>
public double[] <B>nextVector</B>()</PRE>
<DL>
<DD>Generate a correlated random vector.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html#nextVector()">nextVector</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math3.random">RandomVectorGenerator</A></CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>a random vector as an array of double. The returned array
 is created at each call, the caller can do what it wants with it.</DL>
</DD>
</DL>
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